🎪 Singapore Bar Method · Year 6

Concert Fractions

Visual step-by-step using bar models

📋 The Problem

At a concert, 2/9 of the adults equals 7/10 of the children. A total of 249 people attended.

How many adults were there?

1
See the equal parts

2/9 of adults = 7/10 of children — they are equal in value.

Adults
✦
✦
2 parts highlighted = 2/9 of all adults
Children
✦
✦
✦
✦
✦
✦
✦
7 parts highlighted = 7/10 of all children
✦ highlighted parts are EQUAL in value

So: 2 adult-parts = 7 child-parts

2
Pick 14 for the equal part

We need a number that both 2 and 7 divide into evenly (no fractions!).

Multiples of 2
2 4 6 8 10 12 14 ✓
Multiples of 7
7 14 ✓ 21

→ Both share 14. So let the equal part = 14 people.

3
Work backwards to find the ratio
Adults
2 parts = 14 → 1 part = 7 → 9 parts = 63
Children
7 parts = 14 → 1 part = 2 → 10 parts = 20
Total
63
20
Adults: 63 + Children: 20 = 83 total

But the real total is 249, not 83. We need to scale up! →

4
Scale up to 249

How many times bigger is the real concert than our example?

83
our example
×3
249 ÷ 83 = 3
249
real concert

Multiply everything by 3:

Adults
189
Children
60
Total
189
60
📊 Total = 249
189
adults
+
60
children
=
249
total ✅
🎉 Answer
189
adults attended the concert
✓
Check
Verify both conditions
✓ 2/9 × 189 = 42
✓ 7/10 × 60 = 42  ← equal! ✅
✓ 189 + 60 = 249  ← total matches! ✅
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